1. Field of the Invention
The invention relates generally to fixed cutter drill bits used to drill boreholes in subterranean formations. More specifically, the invention relates to methods for modeling the drilling performance of a fixed cutter bit drilling through an earth formation, methods for designing fixed cutter drill bits, methods for optimizing the drilling performance of a fixed cutter drill bit, and to drill bits formed using such methods.
2. Background Art
Fixed cutter bits, such as PDC drill bits, are commonly used in the oil and gas industry to drill well bores. One example of a conventional drilling system for drilling boreholes in subsurface earth formations is shown in FIG. 1. This drilling system includes a drilling rig 10 used to turn a drill string 12 which extends downward into a well bore 14. Connected to the end of the drill string 12 is a fixed cutter drill bit 20.
As shown in FIG. 2, a fixed cutter drill bit 21 typically includes a bit body 22 having an externally threaded connection at one end 24, and a plurality of blades 28 extending from the other end of bit body 22 and forming the cutting surface of the bit 22. A plurality of cutters 29 are attached to each of the blades 28 and extend from the blades to cut through earth formations when the bit 21 is rotated during drilling. The cutters 29 deform the earth formation by scraping and shearing. The cutters 29 may be tungsten carbide inserts, polycrystalline diamond compacts, milled steel teeth, or any other cutting elements of materials hard and strong enough to deform or cut through the formation. Hardfacing (not shown) may also be applied to the cutters 29 and other portions of the bit 21 to reduce wear on the bit 21 and to increase the life of the bit 21 as the bit 21 cuts through earth formations.
Significant expense is involved in the design and manufacture of drill bits and in the drilling of well bores. Having accurate models for predicting and analyzing drilling characteristics of bits can greatly reduce the cost associated with manufacturing drill bits and designing drilling operations because these models can be used to more accurately predict the performance of bits prior to their manufacture and/or use for a particular drilling application. For these reasons, models have been developed and employed for the analysis and design of fixed cutter drill bits.
Two of the most widely used methods for modeling the performance of fixed cutter bits or designing fixed cutter drill bits are disclosed in Sandia Report No. SAN86-1745 by David A. Glowka, printed September 1987 and titled “Development of a Method for Predicting the Performance and Wear of PDC drill Bits” and U.S. Pat. No. 4,815,342 to Bret, et al. and titled “Method for Modeling and Building Drill Bits,” and U.S. Pat. Nos. 5,010789; 5,042,596, and 5,131,478 which are all incorporated herein by reference. While these models have been useful in that they provide a means for analyzing the forces acting on the bit, their accuracy as a reflection of drilling might be improved because these models rely on generalized theoretical approximations (typically some equations) of cutter and formation interaction. A good representation of the actual interactions between a particular drill bit and the particular formation to be drilled is useful for accurate modeling. The accuracy and applicability of assumptions made for all drill bits. All cutters and all earth formations can affect the accuracy of the prediction of the response of an actual drill bit drilling in an earth formation, even though the constants in the relationship are adjusted.
In one popular model for drill bit design it is assumed that the centerline of the drill bit remains aligned with the centerline of the bore hole in which the drill bit is drilling. This type of centerline constrained model might be referred to as a “static model,” even though the model calculates incremental dynamic rotation. The term static as applied to this type of modeling means not varying centerline alignment. In such prior modeling the “conventional wisdom” has been that a stable drill bit design is one with minimum imbalanced cutter forces and a Beta angle (β) between the radial and circumferential components of the resultant imbalance forces that is as small as possible. The theory is based upon vector addition such that for given magnitude imbalance force components, variation from a small β angle to a larger β angle will produce a smaller magnitude total imbalance force vector, even if the magnitudes of the components are not decreased. Thus, starting at a small β angle should result in increased stability, because any increase in the β angle tends to reduce the total imbalance force and moves the drill bit toward a low imbalance force (stable) condition.
A method is desired for modeling the overall cutting action and drilling performance of a fixed cutter bit that takes into consideration a more accurate reflection of the interaction between a drill bit, cutters of the drill bit, and an earth formation during drilling.